A335939 Bi-unitary weird numbers (A292986) that are not exponentially odd numbers (A268335).

5390, 7400, 11830, 20230, 24010, 25270, 37030, 58870, 67270, 95830, 117670, 129430, 154630, 196630, 243670, 260470, 314230, 352870, 373030, 436870, 482230, 491744, 507232, 554470, 658630, 714070, 742630, 801430, 831670, 893830, 1129030, 1201270, 1313830, 1352470

Offset

1,1

Comments

Weird numbers (A006037) that are exponentially odd (A268335) are also bi-unitary weird numbers (A292986), since all of their divisors are bi-unitary.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Mathematica

fun[p_, e_] := If[OddQ[e], (p^(e+1)-1)/(p-1), (p^(e+1)-1)/(p-1)-p^(e/2)]; bsigma[1] = 1; bsigma[n_] := Times @@ (fun @@@ FactorInteger[n]); biuabQ[n_] := bsigma[n] > 2*n; f[n_] := Select[Divisors[n], Function[d, CoprimeQ[d, n/d]]]; bdiv[m_] := Select[Divisors[m], Last@Intersection[f@#, f[m/#]] == 1 &]; bweirdQ[n_] := biuabQ[n] && Module[{d = Most @ bdiv[n], x}, SeriesCoefficient[Series[Product[1 + x^d[[i]], {i, Length[d]}], {x, 0, n}], n] == 0]; expOddQ[n_] := AllTrue[Last /@ FactorInteger[n], OddQ]; Select[Range[1000], !expOddQ[#] && bweirdQ[#] &]

Crossrefs

Intersection of A072587 and A292986.

Cf. A006037, A222266, A268335, A335936, A335938.

Sequence in context: A058325 A224688 A335936 * A328562 A340109 A364991

Adjacent sequences: A335936 A335937 A335938 * A335940 A335941 A335942

Keyword

nonn

Author

Amiram Eldar, Jun 30 2020

Extensions

More terms from Amiram Eldar, Mar 25 2023

Status

approved